DLMF:25.15.E6 (Q7751)

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DLMF:25.15.E6
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    Statements

    Defining formula
    G ⁢ ( χ ) ≡ ∑ r = 1 k χ ⁢ ( r ) ⁢ e 2 ⁢ π ⁢ i ⁢ r / k . equal-by definition 𝐺 𝜒 superscript subscript 𝑟 1 𝑘 𝜒 𝑟 superscript 𝑒 2 𝜋 𝑖 𝑟 𝑘 {\displaystyle{\displaystyle G(\chi)\equiv\sum_{r=1}^{k}\chi(r)e^{2\pi ir/k}.}}
    0 references
    DLMF id
    DLMF:25.15.E6
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10769
    Defining formula
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1cdec
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    Q12168
    Defining formula
    χ ⁢ ( n ) 𝜒 𝑛 {\displaystyle{\displaystyle\chi(n)}}
    xml-id
    C25.S15.XMD1.m1edec
    0 references
     
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